Fourier Optimization and Linear-Algebra-Based Combination of Controls to Improve Bioethanol Production

The development of efficient strategies for optimizing and controlling nonlinear bioprocesses remains a significant challenge due to their complex dynamics and sensitivity to operating conditions. This work addresses the problem by proposing a two-step methodology applied to a laboratory-scale fed-batch bioethanol process. The first step employs a dynamic optimization approach based on Fourier parameterization and orthonormal polynomials, which generates smooth and continuous substrate-feed profiles using only three parameters instead of the ten required by piecewise approaches. The second step introduces a controller formulated through basic linear algebra operations, which ensures accurate trajectory tracking of the optimized state variables. Simulation results demonstrate a 3.65% increase in ethanol concentration at the end of the process, together with an accumulated tracking error of only 0.0189 under nominal conditions. In addition, the closed-loop strategy outperforms open-loop implementation when the initial conditions deviate from their nominal values. These findings highlight that the proposed methodology reduces mathematical complexity and computational effort while producing continuous control profiles suitable for practical application. The combination of optimization and algebraic control thus provides a promising alternative for improving the efficiency of bioethanol-production processes.